"I ask 14 people to buy something, 2 say yes, 12 say no.

Given this happened, what is the probability that the next person I ask will buy something? So that would make it 3 yes, 12 no, 15 total."

The estimate of the probability is 2 / 14. The estimate will have high standard error, since 14 is a small sample size.

"Alternatively, what if I ask 14 people, 0 people buy.

What is the probability that the next person I ask will buy given 0/14 have bought currently?"

If 0 people buy out of 14, then we are dealing with estimating the probability of an extremely rate event. In this case, a sample size of the order of 500-1000 would be necessary to say anything meaningful about the probability.